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reciprocals of the diameters should be plotted. In fact, it is no hard matter to locate on the diagram the reciprocals of the diameters for the screens used; or better still, screen manufacturers could be sufficiently induced to furnish pads of coordinate paper, on which are drawn these lines corresponding with their standard sets of screens.
Two uses are already suggested; the first, determination of crushing resistances of various rocks, and second, the determination of crushing-machine efficiency. Only with a knowledge of the former, can comparisons be made of the operation of two machines at different places. And I believe that this diagram will make necessary some revision of the constants for the crushing resistance of rocks. All tests of rocks have been made on single pieces and the crushing strength determined from an average of a number of tests. Where surface has been determined it is only that of the larger pieces involved in the fracture. No calculations based on the surface of the very fine particles have been made. One thing which will be noticed in nearly every
Thousands of Pounds
n 1615 uistt n ip 9 a i 6 5 4 .3
Bedford limestone.
------(08/yfJc) |    1 . I    |.
Crushed 6 times without
60     120    ie>0   200   240   280   320   360   400   440 Reciprocals of Diameters (Inches)
FIG.  16.—Diagram of crushing tests.
screen analysis that is plotted as a crushing-surface diagram, is that the curve is of the form of a hyperbola, indicating a strong probability of the presence of particles of 1,000 and even 10,000 mesh. Some allowance for the probable area of these very fine particles must be made, and when that is done it will very likely be found that there is a greater area in the —200-mesh particles than in the 4-200-mesh material. There is no question but that the surface of the -200-mesh particles must be considered in crushing calculations. The neglect of this surface, which usually is. not wanted, makes any reasonable comparison impossible between crushing operations that are not very much alike. The agriculturists in the study of soils do not hesitate to measure and discuss particles of clay as small as 0.0002 in. in diameter, and so I see no reason why milling operators should avoid these sizes and talk of colloids as soon as they get past the 200-mesh line. The use of logarithmic paper can be invoked to find out about the —200-mesh particles as I may show later.
Other uses for this diagram should be in the cyanide plant, where time of solution depends upon surface exposed, and the amount of surface is a factor in filtering operations. In the cement industry, surface must play an important part, for each particle of stone or sand or fine material must be coated with cement particles before a good bond can be made. The amount of cement could be made proportional to the area of the diagram for the material used.
In concentrating-mill operations, surface is fully as important in the concentrating department as in crushing operations. It is surface that limits the tonnage that can